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Second-Order Symmetric Duality in Variational Control Problems Over Cone Constraints

ASIA-PACIFIC JOURNAL OF OPERATIONAL RESEARCH 2018年第4期35卷 1850028.1-1850028.1页

作者： Jayswal, Anurag Jha, Shalini Prasad, Ashish Kumar Ahmad, Izhar Indian Sch Mines Indian Inst Technol Dept Appl Math Dhanbad 826004 Jharkhand India Natl Inst Technol Dept Math Jamshedpur 831014 Jharkhand India King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

In the present paper, we introduce a pair of multiobjective second-order symmetric variational control programs over cone constraints and derive weak, strong and converse duality theorems under second-order F-convexity assumption. Moreover, self-duality theorem is also discussed. Our results extend some of the known results in literature.

关键词： multiobjective programming variational control problems second-order F-convexity duality efficient solutions

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Sufficiency and duality for nonsmooth multiobjective programming problems involving generalized (F, α, ρ, θ)-d-V-univex functions

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MATHEMATICAL AND COMPUTER MODELLING 2011年第1-2期53卷 81-90页

作者： Jayswal, Anurag Ahmad, I. Al-Homidan, S. Birla Inst Technol Dept Appl Math Ranchi 835215 Jharkhand India King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia

In this paper, we introduce a new class of generalized (F, alpha, rho, theta)-d-V-univex functions for a nonsmooth multiobjective programming problem. Sufficient optimality conditions under generalized (F, alpha, rho, theta)-d-V-univex functions are established for a feasible solution to be an efficient solution. Appropriate duality theorems for a Mond-Weir-type dual are also presented under the aforesaid assumptions. (C) 2010 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming Generalized (F, alpha, rho, theta)-d-V-univex functions Efficiency Sufficient optimality conditions Duality

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On sufficiency and duality for nonsmooth multiobjective programming problems involving generalized V-r-invex functions

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NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS 2011年第17期74卷 5920-5928页

作者： Ahmad, I. Gupta, S. K. Jayswal, Anurag King Fahd Univ Petr & Minerals Dept Math & Stat Dhahran 31261 Saudi Arabia Indian Inst Technol Dept Math Patna 800013 Bihar India Birla Inst Technol Dept Appl Math Ranchi 835215 Bihar India Aligarh Muslim Univ Dept Math Aligarh 202002 Uttar Pradesh India

In this paper, a class of nonsmooth multiobjective programming problems with inequality constraints is considered. We introduce the concepts of V-r-pseudo-invex, strictly V-r-pseudo-invex and V-r-quasi-invex functions, in which the involved functions are locally Lipschitz. Based upon these generalized V-r-invex functions, sufficient optimality conditions for a feasible point to be an efficient or a weakly efficient solution are derived. Appropriate duality theorems are proved for a Mond-Weir-type dual program of a nonsmooth multiobjective programming under the aforesaid functions. (C) 2011 Elsevier Ltd. All rights reserved.

关键词： multiobjective programming Locally Lipschitz functions Generalized V-r-invex functions Sufficient optimality conditions Duality

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A review of multiobjective programming and its application in quantitative psychology

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JOURNAL OF MATHEMATICAL PSYCHOLOGY 2011年第5期55卷 386-396页

作者： Koehn, Hans-Friedrich Univ Illinois Urbana IL 61801 USA

multiobjective programming, a technique for solving mathematical optimization problems with multiple conflicting objectives, has received increasing attention among researchers in various academic disciplines. A summary of multiobjective programming techniques and a review of their applications in quantitative psychology are provided. (C) 2011 Elsevier Inc. All rights reserved.

关键词： multiobjective programming Quantitative psychology Combinatorial data analysis Three-way data

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Commentary on "On solving a multiobjective fixed charge problem with imprecise fractional objectives"

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APPLIED SOFT COMPUTING 2017年 61卷 681-682页

作者： Kaur, Jagdeep Kumar, Amit Thapar Univ Sch Math Patiala 147004 Punjab India

Upmanyu and Saxena (Applied Soft Computing 40 (2016) 64-69) proposed a method for solving a multiobjective fixed charge problem having multiple fractional objective functions which are all of a fuzzy nature. The aim of this note is to aware the researchers that the method, proposed by Upmanyu and Saxena, is not valid and hence, to propose a method for solving this type of fixed charge problem is still an open challenging research problem. (C) 2017 Elsevier B.V. All rights reserved.

关键词： Fixed charge problem multiobjective programming Fractional programming Fuzzy objective function

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Comparative Analysis of Load-Shaping-Based Privacy Preservation Strategies in a Smart Grid

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IEEE TRANSACTIONS ON INDUSTRIAL INFORMATICS 2017年第6期13卷 3226-3235页

作者： Kement, Cihan Emre Gultekin, Hakan Tavli, Bulent Girici, Tolga Uludag, Suleyman TOBB Univ Econ & Technol Dept Elect & Elect Engn TR-06560 Ankara Turkey TOBB Univ Econ & Technol Dept Ind Engn TR-06560 Ankara Turkey Univ Michigan Dept Comp Sci Engn & Phys Flint MI 48502 USA

A key enabler for the smart grid is the fine-grained monitoring of power utilization. Although such a mechanism is helpful in the optimization of the whole electricity generation, distribution, and consumption cycle, it also creates opportunities for the potential adversaries in deducing the activities and habits of the subscribers. In fact, by utilizing the standard and readily available tools of nonintrusive load monitoring (NILM) techniques on the metered electricity data, many details of customers' personal lives can be easily discovered. Therefore, prevention of such adversarial exploitations is of utmost importance for privacy protection. One strong privacy preservation approach is the modification of the metered data through the use of on-site storage units in conjunction with renewable energy resources. In this study, we introduce a novel mathematical programming framework to model eight privacy-enhanced power-scheduling strategies inspired and elicited from the literature. We employ all the relevant techniques for the modification of the actual electricity utilization (i.e., on-site battery, renewable energy resources, and appliance load moderation). Our evaluation framework is the first in the literature, to the best of our knowledge, for a comprehensive and fair comparison of the load-shaping techniques for privacy preservation. In addition to the privacy concerns, we consider monetary cost and disutility of the users in our objective functions. Evaluation results show that privacy preservation strategies in the literature differ significantly in terms of privacy, cost, and disutility metrics.

关键词： Goal programming load shaping mixed-integer programming (MIP) mixed-integer quadratic programming (MIQP) multiobjective programming nonintrusive load monitoring (NILM) privacy renewable energy smart grid

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Partitioning methods for pruning the Pareto set with application to multiobjective allocation of a cross-trained workforce

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COMPUTERS & INDUSTRIAL ENGINEERING 2017年 111卷 29-38页

作者： Brusco, Michael J. Florida State Univ Coll Business Dept Business Analyt Informat Syst & Supply Chain Tallahassee FL 32306 USA

The Pareto (or nondominated set) for a multiobjective optimization problem is often of nontrivial size, and the decision maker may have a difficult time establishing objective criterion weights to select a solution. In light of these issues, clustering or partitioning methods can be of considerable value for pruning the Pareto set and limiting the decision to a few choice exemplars. A three-stage approach is proposed. In stage one, a variance-to-range measure is used to normalize the criterion function values. In stage two, maximum split partitioning and p-median partitioning are each applied to the normalized measures, thus producing two partitions of the Pareto set and two sets of exemplars. Finally, in stage three, the union of the exemplars obtained by the two partitioning methods is accepted as the final set of exemplars. The partitioning methods are compared within the context of multiobjective allocation of a cross-trained workforce to achieve both operational and human resource objectives. (C) 2017 Elsevier Ltd. All rights reserved.

关键词： Partitioning Pruned Pareto sets multiobjective programming Workforce allocation

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Random approximations in multiobjective optimization

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MATHEMATICAL programming 2017年第1-2期164卷 29-53页

作者： Vogel, Silvia Ilmenau Univ Technol Weimarer Str 25 D-98693 Ilmenau Germany

Often decision makers have to cope with a programming problem with unknown quantitities. Then they will estimate these quantities and solve the problem as it then appears-the 'approximate problem'. Thus there is a need to establish conditions which will ensure that the solutions to the approximate problem will come close to the solutions to the true problem in a suitable manner. Confidence sets, i.e. sets that cover the true sets with a given prescribed probability, provide useful quantitative information. In this paper we consider multiobjective problems and derive confidence sets for the sets of efficient points, weakly efficient points, and the corresponding solution sets. Besides the crucial convergence conditions for the objective and/or constraint functions, one approach for the derivation of confidence sets requires some knowledge about the true problem, which may be not available. Therefore also another method, called relaxation, is suggested. This approach works without any knowledge about the true problem. The results are applied to the Markowitz model of portfolio optimization.

关键词： multiobjective programming Stability Confidence sets Estimated functions Relaxation Markowitz model

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Portfolio selection in the Spanish stock market by interactive multiobjective programming

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TOP 2011年第1期19卷 213-231页

作者： Rodriguez, Rafael Luque, Mariano Gonzalez, Mercedes Univ Malaga Fac Econ Dept Appl Econ Math E-29071 Malaga Spain

This study examines new versions of two interactive methods to address multiobjective problems, the aim of which is to enable the decision maker to reach a solution within the range of those considered efficient in a portfolio selection model, in which several objectives are pursued concerning risk and return and given that these are clearly conflicting objectives, the profile of the model proposed is multicriteria. Normally the range of efficient portfolios is fairly extensive thus making the selection of a single one an onerous task. In order to facilitate this process, interactive methods are used aimed at guiding the decision maker towards the optimal solution based on his preferences. Several adaptations were carried out on the original methods in order to facilitate the interactive process, improving the quality of the obtained portfolios, and these were applied to data obtained from the Madrid Stock Market, interaction taking place with two decision makers, one of whom was more aggressive than the other in their selections made.

关键词： Portfolio selection multiobjective programming Interactive methods Reference point method Multiple criteria decision making

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Proper Efficiency and Tradeoffs in Multiple Criteria and Stochastic Optimization

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MATHEMATICS OF OPERATIONS RESEARCH 2017年第1期42卷 119-134页

作者： Engau, Alexander Univ Colorado Denver Math & Stat Sci Denver CO 80202 USA

The mathematical equivalence between linear scalarizations in multiobjective programming and expected- value functions in stochastic optimization suggests to investigate and establish further conceptual analogies between these two areas. In this paper, we focus on the notion of proper efficiency that allows us to provide a first comprehensive analysis of solution and scenario tradeoffs in stochastic optimization. In generalization of two standard characterizations of properly efficient solutions using weighted sums and augmented weighted Tchebycheff norms for finitely many criteria, we show that these results are generally false for infinitely many criteria. In particular, these observations motivate a slightly modified definition to prove that expected- value optimization over continuous random variables still yields bounded tradeoffs almost everywhere in general. Further consequences and practical implications of these results for decision-making under uncertainty and its related theory and methodology of multiple criteria, stochastic and robust optimization are discussed.

关键词： proper efficiency tradeoffs multicriteria optimization multiobjective programming stochastic optimization stochastic programming robust optimization linear scalarization weighted sum method augmented Tchebycheff norm expected value function decision making under uncertainty

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